Man, you could read an entire book on this, its a science in itself.
Basically, its a device that atomizes/mixes your fuel with incoming air. The more your step on the gas, the more the carb opens and sucks in more air and fuel.
The barrel term refers to the carburetor opening. A standard carb is 2 barrel. A 4 barrel has 2 more openings, which gets you essentially more power as it lets in more air.
Inside the carb you have needles and jets that are set to meter gas and whatnot.